Skip to main content
Erschienen in: Meccanica 1/2014

01.01.2014

Dynamics of a linear system with time-dependent mass and a coupled light mass with non-smooth potential

verfasst von: C.-H. Lamarque, A. Ture Savadkoohi, Z. Dimitrijevic

Erschienen in: Meccanica | Ausgabe 1/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Multi-scale dynamics of two coupled oscillators, the linear one with varying mass and a non-smooth light system is studied. The light system, namely nonlinear energy sink (NES) is implemented for passively controlling the linear system against external impulses and/or forces. Obtained invariant manifold of the system at fast time scale let us explain the system behavior during its transient and steady-state regime while predicted dynamics of the system at slow time scale let us detect the positions of fixed and fold singularities by explanation of its behavior.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems I. Springer, Berlin Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems I. Springer, Berlin
2.
Zurück zum Zitat Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems II. Springer, Berlin Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems II. Springer, Berlin
3.
Zurück zum Zitat Vakakis AF (2001) Inducing passive nonlinear energy sinks in vibrating systems. J Vib Acoust 123:324–332 CrossRef Vakakis AF (2001) Inducing passive nonlinear energy sinks in vibrating systems. J Vib Acoust 123:324–332 CrossRef
4.
Zurück zum Zitat Gendelman OV, Manevitch LI, Vakakis AF, M’Closkey R (2001) Energy pumping in nonlinear mechanical oscillators, I: dynamics of the underlying Hamiltonian systems. J Appl Mech 68:34–41 CrossRefMATHMathSciNet Gendelman OV, Manevitch LI, Vakakis AF, M’Closkey R (2001) Energy pumping in nonlinear mechanical oscillators, I: dynamics of the underlying Hamiltonian systems. J Appl Mech 68:34–41 CrossRefMATHMathSciNet
5.
Zurück zum Zitat Vakakis AF, Gendelman OV (2001) Energy pumping in nonlinear mechanical oscillators, II: resonance capture. J Appl Mech 68:42–48 CrossRefMATHMathSciNet Vakakis AF, Gendelman OV (2001) Energy pumping in nonlinear mechanical oscillators, II: resonance capture. J Appl Mech 68:42–48 CrossRefMATHMathSciNet
6.
Zurück zum Zitat Gendelman OV, Lamarque C-H (2005) Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium. Chaos Solitons Fractals 24:501–509 ADSCrossRefMATHMathSciNet Gendelman OV, Lamarque C-H (2005) Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium. Chaos Solitons Fractals 24:501–509 ADSCrossRefMATHMathSciNet
7.
Zurück zum Zitat Manevitch LI, Musienko AI, Lamarque C-H (2007) New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems. Meccanica 42:77–83 CrossRefMATHMathSciNet Manevitch LI, Musienko AI, Lamarque C-H (2007) New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems. Meccanica 42:77–83 CrossRefMATHMathSciNet
8.
Zurück zum Zitat Avramov KV, Gendelman OV (2010) On interaction of vibrating beam with essentially nonlinear absorber. Meccanica 45:355–365 CrossRefMATHMathSciNet Avramov KV, Gendelman OV (2010) On interaction of vibrating beam with essentially nonlinear absorber. Meccanica 45:355–365 CrossRefMATHMathSciNet
9.
Zurück zum Zitat Shiroky IB, Gendelman OV (2008) Essentially nonlinear vibration absorber in a parametrically excited system. J Appl Math Mech 88:573–596 MATHMathSciNet Shiroky IB, Gendelman OV (2008) Essentially nonlinear vibration absorber in a parametrically excited system. J Appl Math Mech 88:573–596 MATHMathSciNet
10.
Zurück zum Zitat Vaurigaud B, Manevitch LI, Lamarque C-H (2011) Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer. J Sound Vib 330:2580–2595 ADSCrossRef Vaurigaud B, Manevitch LI, Lamarque C-H (2011) Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer. J Sound Vib 330:2580–2595 ADSCrossRef
11.
Zurück zum Zitat Vaurigaud B, Ture Savadkoohi A, Lamarque C-H (2011) Targeted energy transfer with parallel nonlinear energy sinks, part I: design theory and numerical results, nonlinear dynamics. Nonlinear Dyn 66:763–780 CrossRefMATHMathSciNet Vaurigaud B, Ture Savadkoohi A, Lamarque C-H (2011) Targeted energy transfer with parallel nonlinear energy sinks, part I: design theory and numerical results, nonlinear dynamics. Nonlinear Dyn 66:763–780 CrossRefMATHMathSciNet
12.
Zurück zum Zitat McFarland DM, Kerschen G, Kowtko JJ, Lee YS, Bergman LA, Vakakis AF (2005) Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J Acoust Soc Am 118:791–799 ADSCrossRef McFarland DM, Kerschen G, Kowtko JJ, Lee YS, Bergman LA, Vakakis AF (2005) Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J Acoust Soc Am 118:791–799 ADSCrossRef
13.
Zurück zum Zitat Kerschen G, Kowtko JJ, McFarland DM, Bergman LA, Vakakis AF (2007) Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators. Nonlinear Dyn 47:285–309 CrossRefMATHMathSciNet Kerschen G, Kowtko JJ, McFarland DM, Bergman LA, Vakakis AF (2007) Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators. Nonlinear Dyn 47:285–309 CrossRefMATHMathSciNet
14.
Zurück zum Zitat Kerschen G, Kowtko JJ, McFarland DM, Lee YS, Bergman LA, Vakakis AF (2007) Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity. J Sound Vib 299:822–838 ADSCrossRef Kerschen G, Kowtko JJ, McFarland DM, Lee YS, Bergman LA, Vakakis AF (2007) Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity. J Sound Vib 299:822–838 ADSCrossRef
15.
Zurück zum Zitat Gourdon E, Alexander NA, Taylor CA, Lamarque C-H, Pernot S (2007) Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J Sound Vib 300:522–551 ADSCrossRef Gourdon E, Alexander NA, Taylor CA, Lamarque C-H, Pernot S (2007) Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J Sound Vib 300:522–551 ADSCrossRef
16.
Zurück zum Zitat Lee YS, Kerschen G, McFarland DM, Hill WJ, Nichkawde C, Strganac TW, Bergman LA, Vakakis AF (2007) Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments. AIAA J 45:2391–2400 ADSCrossRef Lee YS, Kerschen G, McFarland DM, Hill WJ, Nichkawde C, Strganac TW, Bergman LA, Vakakis AF (2007) Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments. AIAA J 45:2391–2400 ADSCrossRef
17.
Zurück zum Zitat Lee YS, Vakakis AF, Bergman LA, McFarland DM, Kerschen G, Nucera F, Tsakirtzis S, Panagopoulos PN (2008) Passive non-linear targeted energy transfer and its applications to vibration absorption: a review. Multibody Syst Dyn 222:77–134 Lee YS, Vakakis AF, Bergman LA, McFarland DM, Kerschen G, Nucera F, Tsakirtzis S, Panagopoulos PN (2008) Passive non-linear targeted energy transfer and its applications to vibration absorption: a review. Multibody Syst Dyn 222:77–134
18.
Zurück zum Zitat Lee YS, Tsakirtzis S, Vakakis AF, Bergman LA, McFarland DM (2011) A time-domain nonlinear system identification method based on multiscale dynamic partitions. Meccanica 46:625–649 CrossRefMATHMathSciNet Lee YS, Tsakirtzis S, Vakakis AF, Bergman LA, McFarland DM (2011) A time-domain nonlinear system identification method based on multiscale dynamic partitions. Meccanica 46:625–649 CrossRefMATHMathSciNet
19.
Zurück zum Zitat Ture Savadkoohi A, Vaurigaud B, Lamarque C-H, Pernot S (2012) Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments. Nonlinear Dyn 67:37–46 CrossRefMATHMathSciNet Ture Savadkoohi A, Vaurigaud B, Lamarque C-H, Pernot S (2012) Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments. Nonlinear Dyn 67:37–46 CrossRefMATHMathSciNet
20.
Zurück zum Zitat Nucera F, Vakakis AF, McFarland DM, Bergman LA, Kerschen G (2007) Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn 50:651–677 CrossRefMATH Nucera F, Vakakis AF, McFarland DM, Bergman LA, Kerschen G (2007) Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn 50:651–677 CrossRefMATH
21.
Zurück zum Zitat Lee YS, Nucera F, Vakakis AF, McFarland DM, Bergman LA (2009) Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Physica D 238:1868–1896 ADSCrossRefMATH Lee YS, Nucera F, Vakakis AF, McFarland DM, Bergman LA (2009) Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Physica D 238:1868–1896 ADSCrossRefMATH
22.
Zurück zum Zitat Gendelman OV (2008) Targeted energy transfer in systems with non-polynomial nonlinearity. J Sound Vib 315:732–745 ADSCrossRef Gendelman OV (2008) Targeted energy transfer in systems with non-polynomial nonlinearity. J Sound Vib 315:732–745 ADSCrossRef
23.
Zurück zum Zitat Schmidt F, Lamarque C-H (2010) Energy pumping for mechanical systems involving non-smooth Saint-Venant terms. Int J Non-Linear Mech 45:866–875 CrossRef Schmidt F, Lamarque C-H (2010) Energy pumping for mechanical systems involving non-smooth Saint-Venant terms. Int J Non-Linear Mech 45:866–875 CrossRef
24.
Zurück zum Zitat Lamarque C-H, Gendelman OV, Ture Savadkoohi A, Etcheverria E (2011) Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech 221:175–200 CrossRefMATH Lamarque C-H, Gendelman OV, Ture Savadkoohi A, Etcheverria E (2011) Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech 221:175–200 CrossRefMATH
25.
Zurück zum Zitat Lamarque C-H, Ture Savadkoohi A, Etcheverria E, Dimitrijevic Z (2012) Multi-scales dynamics of two coupled non-smooth systems. Int J Bifurc Chaos 22:1250295 CrossRefMathSciNet Lamarque C-H, Ture Savadkoohi A, Etcheverria E, Dimitrijevic Z (2012) Multi-scales dynamics of two coupled non-smooth systems. Int J Bifurc Chaos 22:1250295 CrossRefMathSciNet
26.
Zurück zum Zitat Ture Savadkoohi A, Lamarque C-H, Dimitrijevic Z (2012) Vibratory energy exchange between a linear and a non-smooth system in the presence of the gravity. Nonlinear Dyn 70:1473–1483 CrossRefMathSciNet Ture Savadkoohi A, Lamarque C-H, Dimitrijevic Z (2012) Vibratory energy exchange between a linear and a non-smooth system in the presence of the gravity. Nonlinear Dyn 70:1473–1483 CrossRefMathSciNet
27.
Zurück zum Zitat Van Horssen WT, Pischanskyy OV (2011) On the stability properties of a damped oscillator with a periodically time-varying mass. J Sound Vib 330:3257–3269 ADSCrossRef Van Horssen WT, Pischanskyy OV (2011) On the stability properties of a damped oscillator with a periodically time-varying mass. J Sound Vib 330:3257–3269 ADSCrossRef
28.
Zurück zum Zitat McComber P, Paradis A (1998) A cable galloping model for thin ice accretions. Atmos Res 46:13–25 CrossRef McComber P, Paradis A (1998) A cable galloping model for thin ice accretions. Atmos Res 46:13–25 CrossRef
29.
Zurück zum Zitat Manevitch LI (1970) General motion of a variable mass flexible rocket with internal flow. J Spacecr Rockets 7:186–195 ADSCrossRef Manevitch LI (1970) General motion of a variable mass flexible rocket with internal flow. J Spacecr Rockets 7:186–195 ADSCrossRef
30.
Zurück zum Zitat Pischanskyy OV, Van Horssen WT (2012) On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass. J Sound Vib 331:1887–1897 ADSCrossRef Pischanskyy OV, Van Horssen WT (2012) On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass. J Sound Vib 331:1887–1897 ADSCrossRef
31.
Zurück zum Zitat Manevitch LI (2001) The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn 25:95–109 CrossRefMATHMathSciNet Manevitch LI (2001) The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn 25:95–109 CrossRefMATHMathSciNet
32.
Zurück zum Zitat Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York MATH Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York MATH
33.
Zurück zum Zitat Starosvetsky Y, Gendelman OV (2008) Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Physica D 237:1719–1733 ADSCrossRefMATHMathSciNet Starosvetsky Y, Gendelman OV (2008) Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Physica D 237:1719–1733 ADSCrossRefMATHMathSciNet
Metadaten
Titel
Dynamics of a linear system with time-dependent mass and a coupled light mass with non-smooth potential
verfasst von
C.-H. Lamarque
A. Ture Savadkoohi
Z. Dimitrijevic
Publikationsdatum
01.01.2014
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 1/2014
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9778-8

Weitere Artikel der Ausgabe 1/2014

Meccanica 1/2014 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.